I had the same problem. Bought some mildew remover from a boating shop. Took several applications (applied, scrubbed with a brush, waited some minutes, and rinsed). I think it was basically a bleach/water mix.

I couldn't believe the difference. The top virtually looks new (I honestly don't think it's been this white since I owned it!)

If your top is not white, I would try it in the least conspicuous place first.